Question

Question #f6ba4

Answer 1

it's EVEN if f(-x) = f(x) for all x in the domain

Explanation:

...because one definition of an even function is that its graph is symmetrical about the y axis.

If you can fold the graph along the y axis, and lay the right side of the paper over the left, and the graph superimposes on itself, it's an even function.

Some examples:

`y = x^2` is EVEN, while `y = x^3` is ODD.

`y = cos(x)` is EVEN, while `y = sin(x)` is ODD.

GOOD LUCK

Update: the definition is only complete if you add:

a function is ODD if f(-x) = -f(x) for all x in the domain.

So, `y = x^3` is odd by that definition, and `y = e^x` is NEITHER.

GOOD LUCK

Answer 2

An even function has the same y value for a given x and -x
An odd function has a y value for a given x and a -y value for -x. Otherwise, the graph is neither.

Explanation:

Here is a graph of an even function.

graph{cos(x) [-10, 10, -5, 5]}

Please observe that it has the same y value for `x = 1` and `x = -1`.

Here is a graph of an odd function:

graph{sin(x) [-10, 10, -5, 5]}

Please observe that y value corresponding to `x = 1` and observe that is has same y value but negative for `x = -1`.

Here is a graph of a function that is neither.

graph{e^x [-10, 10, -5, 5]}